The results show that quantum optimal control techniques, especially GRAPE and the PMP, are versatile tools to design gates on Rydberg atoms. In this work, only gates that make use of a single Rydberg state per atom and that operate in the blockade regime were considered. While most gates in current experiments are of this kind, it is known that more robust gates can be achieved when using several Rydberg states per atom [1]}, [2]}, and ultrafast gates can be achieved by operating outside of the Rydberg blockade regime [3]}. We expect that quantum optimal control techniques can also be used to improve these gates.
